The Relational Data Model

Relationships Among Normal Forms

As we have pointed out, 4NF implies BCNF, which in turn implies 3NF. Therefore, the sets of relation schemas (including dependencies) satisfying the three normal forms are related as in the following figure. That is, if a relation with certain dependencies is in 4NF, it is also in

Decomposition into Fourth Normal Form

The 4NF decomposition algorithm is quite similar to the BCNF decomposition algorithm. We find a 4NF violation, say A1A2 . . . An → B1B2 . . . Bm , where {A1, A2, . . . , An} is not a superkey. Note this MVD could be a true MVD, or it could be derived from the equivalent FD A1A2 . . . An

Fourth Normal Form

The redundancy that we found in "Multivalued Dependencies" to be caused by MVD's can be removed if we use these dependencies in a new decomposition algorithm for relations. In this section we shall introduce a new normal form, called "fourth normal form". In this normal form,

Reasoning About Multivalued Dependencies

There are a many rules about MVD's that are similar to the rules we learned for FD's in "Rules About Functional Dependencies". For instance, MVD's obey

Definition of Multivalued Dependencies

A multivalued dependency (often abbreviated MVD) is a statement about some relation R that when you fix the values for one set of attributes, then the values in certain other attributes are independent of the values of all the other attributes in the relation. More specifically, we say the MVD

Multivalued Dependencies

A "multivalued dependency" is an assertion that two attributes or sets of attributes are independent of one another. This condition is, as we shall see, an overview of the notion of a functional dependency, in the sense that every FD implies a corresponding multivalued dependency.

Third Normal Form

Sometimes, one encounters a relation schema and its FD's that are not in BCNF but that one doesn't want to decompose further. The following example is typical.

Recovering Information from a Decomposition

Let us now turn our attention to the question of why the decomposition algorithm of "Decomposition into BCNF" preserves the information that was included in the original relation. The idea is that if we follow this algorithm, then the projections of the original tuples can be "joined"

Decomposition into BCNF

By frequently selecting appropriate decompositions, we can break any relation schema into a collection of subsets of its attributes with the following important properties:

Boyce-Codd Normal Form

The objective of decomposition is to replace a relation by several that do not exhibit anomalies. There is, it turns out, a simple condition under which the anomalies discussed above can be guaranteed not to exist. This condition is called Boyce-Codd

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